What is X in the sequence 1, 3, 6, 11, 18, X, 42?

The pattern in the sequence is determined by the differences between consecutive terms. Let's find the differences: 3 - 1 = 2 6 - 3 = 3 11 - 6 = 5 18 - 11 = 7 The differences are 2, 3, 5, 7. This is the sequence of prime numbers. Following this pattern, the next prime number after 7 is 11. So, X should be 18 + 11 = 29. To verify, the next prime number after 11 is 13. If X is 29, then the next term should be 29 + 13 = 42. This matches the given sequence. Therefore, X = 29. Analyzing the options: A) 26: If X were 26, the difference from 18 would be 8, which is not a prime number in the sequence. B) 27: If X were 27, the difference from 18 would be 9, which is not a prime number in the sequence. C) 29: If X were 29, the difference from 18 would be 11, which is the next prime number in the sequence. This fits the pattern. D) 30: If X were 30, the difference from 18 would be 12, which is not a prime number in the sequence. The final answer is C.